1. ## two calculus questions

Hi,

Could you please show me how to solve these two questions? Thank you very much.

1. Determine whether lim [sin (x^2+ y^2+z^2) ]/ sqrt(x^2+ y^2+z^2) as (x,y,z) -> (0,0,0) exists. If so, find its value.

2. Let f(x,y) = xyln(x^2+y^2).
Is it possible to define f(0,0) so that f will be continuous at (0,0)?

2. Originally Posted by littlemu
Hi,

Could you please show me how to solve these two questions? Thank you very much.

1. Determine whether lim [sin (x^2+ y^2+z^2) ]/ sqrt(x^2+ y^2+z^2) as (x,y,z) -> (0,0,0) exists. If so, find its value....
Hi, µ,

I've attached my calculations:

3. Originally Posted by littlemu
Hi,

Could you please show me how to solve these two questions? Thank you very much....

2. Let f(x,y) = xyln(x^2+y^2).
Is it possible to define f(0,0) so that f will be continuous at (0,0)?
Hi,

I've attached the calculations and the graph of the function: